Exploratory Analysis
Comparison with Gandal dataset
The datasets are quite similar in general
Autism samples have higher levels of expression
Overexpressed genes have a higher level of expression than under expressed genes (again, I think it’s weird)
DE genes separate into two clouds based on the sign of their lfc
This dataset has five times less DE genes than Gandal, with only 5% of its genes being DE
There don’t seem to be underlying distributions when plotting genes by mean expression or by standard deviation anymore
#setwd('/afs/inf.ed.ac.uk/user/s17/s1725186/Documents/PhD-InitialExperiments/Gupta/R_Markdowns')
library(tidyverse) ; library(reshape2) ; library(glue) ; library(plotly) ; library(plotlyutils)
library(RColorBrewer) ; library(viridis) ; require(gridExtra) ; library(GGally)
library(Rtsne)
library(ClusterR)
library(DESeq2)Load preprocessed dataset (preprocessing code in 19_11_14_data_preprocessing.Rmd)
# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.frame
# GO Neuronal annotations
GO_annotations = read.csv('./../../FirstYearReview/Data/GO_annotations/genes_GO_annotations.csv')
GO_neuronal = GO_annotations %>% filter(grepl('neuron', go_term)) %>%
mutate('ID'=as.character(ensembl_gene_id)) %>%
dplyr::select(-ensembl_gene_id) %>% distinct(ID) %>%
mutate('Neuronal'=1)
# Update DE_info with Neuronal information
DE_info = DE_info %>% mutate('ID'=rownames(.)) %>% left_join(GO_neuronal, by='ID') %>%
mutate(Neuronal=ifelse(is.na(Neuronal), 0, Neuronal)) %>%
mutate(significant=padj<0.05 & !is.na(padj))All samples together
- The distributions seem pretty homogeneous
plot_data = data.frame('ID'=rownames(datExpr), 'Mean'=rowMeans(datExpr))
p1 = ggplotly(plot_data %>% ggplot(aes(Mean)) + geom_density(color='#0099cc', fill='#0099cc', alpha=0.3) +
scale_x_log10() + theme_minimal())
plot_data = data.frame('ID'=colnames(datExpr), 'Mean'=colMeans(datExpr))
p2 = ggplotly(plot_data %>% ggplot(aes(Mean)) + geom_density(color='#0099cc', fill='#0099cc', alpha=0.3) +
theme_minimal() + ggtitle('Mean expression density by gene (left) and by Sample (right)'))
subplot(p1, p2, nrows=1)rm(p1, p2, plot_data)Genes with a neuronal function have a larger mean than genes without it, although the difference is not big
Autism samples tend to have a higher mean expression than the control group, but, opposite to the Gandal dataset, this time they have a lower spread
plot_data = data.frame('ID'=rownames(datExpr), 'Mean'=rowMeans(datExpr)) %>%
left_join(GO_neuronal, by='ID') %>% mutate('Neuronal'=ifelse(is.na(Neuronal),F,T))
p1 = plot_data %>% ggplot(aes(Mean, color=Neuronal, fill=Neuronal)) + geom_density(alpha=0.3) +
scale_x_log10() + theme_minimal() + theme(legend.position='bottom') +
ggtitle('Mean expression density by gene')
plot_data = data.frame('ID'=colnames(datExpr), 'Mean'=colMeans(datExpr)) %>%
left_join(datMeta, by=c('ID'='ID'))
p2 = plot_data %>% ggplot(aes(Mean, color=Diagnosis, fill=Diagnosis)) + geom_density(alpha=0.3) +
theme_minimal() + theme(legend.position='bottom') +
ggtitle('Mean expression density by Sample')
grid.arrange(p1, p2, nrow=1)
rm(GO_annotations, plot_data, p1, p2)ASD vs CTL
In general there doesn’t seem to be a lot of variance in mean expression between autism and control samples by gene.
plot_data = data.frame('ID'=rownames(datExpr),
'ASD'=rowMeans(datExpr[,datMeta$Diagnosis=='ASD']),
'CTL'=rowMeans(datExpr[,datMeta$Diagnosis!='ASD']))
plot_data %>% ggplot(aes(ASD,CTL)) + geom_point(alpha=0.1, color='#0099cc') +
geom_abline(color='gray') + ggtitle('Mean expression ASD vs CTL') + theme_minimal()
There doesn’t seem to be a noticeable difference between mean expression by gene between diagnosis groups
Samples with autism tend to have a narrower dispersion of mean expression with higher values than the control group (as we had already seen above)
plot_data = rbind(data.frame('Mean'=rowMeans(datExpr[,datMeta$Diagnosis=='ASD']), 'Diagnosis'='ASD'),
data.frame('Mean'=rowMeans(datExpr[,datMeta$Diagnosis!='ASD']), 'Diagnosis'='CTL')) %>%
mutate('Diagnosis'=factor(Diagnosis, levels=c('CTL','ASD')))
p1 = ggplotly(plot_data %>% ggplot(aes(Mean, color=Diagnosis, fill=Diagnosis)) +
geom_density(alpha=0.3) + scale_x_log10() + theme_minimal())
plot_data = rbind(data.frame('Mean'=colMeans(datExpr[,datMeta$Diagnosis=='ASD']), 'Diagnosis'='ASD'),
data.frame('Mean'=colMeans(datExpr[,datMeta$Diagnosis!='ASD']), 'Diagnosis'='CTL')) %>%
mutate('Diagnosis'=factor(Diagnosis, levels=c('CTL','ASD')))
p2 = ggplotly(plot_data %>% ggplot(aes(Mean, color=Diagnosis, fill=Diagnosis)) +
geom_density(alpha=0.3) + theme_minimal() +
ggtitle('Mean expression by Gene (left) and by Sample (right) grouped by Diagnosis'))
subplot(p1, p2, nrows=1)rm(p1, p2, plot_data)Visualisations
Samples
PCA
The first principal component seems to separate almost perfectly the two diagnosis
pca = datExpr %>% t %>% prcomp
plot_data = data.frame('ID'=colnames(datExpr), 'PC1' = pca$x[,1], 'PC2' = pca$x[,2]) %>%
left_join(datMeta, by=c('ID'='ID')) %>%
dplyr::select('ID','PC1','PC2','Diagnosis') %>%
mutate('Diagnosis'=factor(Diagnosis, levels=c('CTL','ASD')))
plot_data %>% ggplot(aes(PC1, PC2, color=Diagnosis)) + geom_point() + theme_minimal() + ggtitle('PCA') +
xlab(paste0('PC1 (',round(100*summary(pca)$importance[2,1],1),'%)')) +
ylab(paste0('PC2 (',round(100*summary(pca)$importance[2,2],1),'%)'))
rm(pca, plot_data)MDS
Looks exactly the same as the PCA visualisation, just inverting both axis
d = datExpr %>% t %>% dist
fit = cmdscale(d, k=2)
plot_data = data.frame('ID'=colnames(datExpr), 'C1'=fit[,1], 'C2'=fit[,2]) %>%
left_join(datMeta, by=c('ID'='ID')) %>%
dplyr::select('C1','C2','Diagnosis') %>%
mutate('Diagnosis'=factor(Diagnosis, levels=c('CTL','ASD')))
plot_data %>% ggplot(aes(C1, C2, color=Diagnosis)) + geom_point() + theme_minimal() + ggtitle('MDS')
rm(d, fit, plot_data)t-SNE
Higher perplexities seem to capture the difference between diagnosis better, although at the end they seem to be capturing another pattern as well, since the samples seem to be grouped in pairs
perplexities = c(2,5,10,30)
ps = list()
for(i in 1:length(perplexities)){
set.seed(123)
tsne = datExpr %>% t %>% Rtsne(perplexity=perplexities[i])
plot_data = data.frame('ID'=colnames(datExpr), 'C1'=tsne$Y[,1], 'C2'=tsne$Y[,2]) %>%
left_join(datMeta, by=c('ID'='ID')) %>%
dplyr::select('C1','C2','Diagnosis','Subject_ID') %>%
mutate('Diagnosis'=factor(Diagnosis, levels=c('CTL','ASD')))
ps[[i]] = plot_data %>% ggplot(aes(C1, C2, color=Diagnosis)) + geom_point() + theme_minimal() +
ggtitle(paste0('Perplexity=',perplexities[i])) + theme(legend.position='none')
}
grid.arrange(grobs=ps, nrow=2)
rm(ps, perplexities, tsne, i)In the Gandal dataset, the higher perplexity values managed to capture the subject the samples belonged to, but it doesn’t seem to do it with this new dataset
ggplotly(plot_data %>% ggplot(aes(C1, C2, color=Subject_ID)) + geom_point(aes(id=Subject_ID)) + theme_minimal() +
theme(legend.position='none') + ggtitle('t-SNE Perplexity=30 coloured by Subject ID'))rm(plot_data)Genes
PCA
First Principal Component explains over 96% of the total variance (Less than Gandal’s)
There’s a really strong correlation between the mean expression of a gene and the 1st principal component
pca = datExpr %>% prcomp
plot_data = data.frame( 'PC1' = pca$x[,1], 'PC2' = pca$x[,2], 'MeanExpr'=rowMeans(datExpr))
plot_data %>% ggplot(aes(PC1, PC2, color=MeanExpr)) + geom_point(alpha=0.3) + theme_minimal() +
scale_color_viridis() + ggtitle('PCA') +
xlab(paste0('PC1 (',round(100*summary(pca)$importance[2,1],1),'%)')) +
ylab(paste0('PC2 (',round(100*summary(pca)$importance[2,2],1),'%)'))
rm(pca, plot_data)t-SNE
Higher perplexities seem to capture the difference between diagnosis better, although at the end they seem to be capturing another pattern as well, since the samples seem to be grouped in pairs
perplexities = c(1,2,5,10,50,100)
ps = list()
for(i in 1:length(perplexities)){
tsne = read.csv(paste0('./../Visualisations/tsne_perplexity_',perplexities[i],'.csv'))
plot_data = data.frame('C1'=tsne[,1], 'C2'=tsne[,2], 'MeanExpr'=rowMeans(datExpr))
ps[[i]] = plot_data %>% ggplot(aes(C1, C2, color=MeanExpr)) + geom_point(alpha=0.5) + theme_minimal() +
scale_color_viridis() + ggtitle(paste0('Perplexity=',perplexities[i])) + theme(legend.position='none')
}
grid.arrange(grobs=ps, nrow=2)
rm(perplexities, ps, tsne, i)Differential Expression Analysis
Only 747 genes (~5% vs ~26% in Gandal’s dataset) are significant using a threshold of 0.05 for the adjusted p-value and a without a log Fold Change threshold (keeping the null hypothesis \(H_0: lfc=0\))
All genes don’t have an adjusted p-value (no NAs)
table(DE_info$padj<0.05, useNA='ifany')##
## FALSE TRUE <NA>
## 9641 747 3871p = DE_info %>% ggplot(aes(log2FoldChange, padj, color=padj<0.05)) + geom_point(alpha=0.2) +
scale_y_sqrt() + xlab('log2 Fold Change') + ylab('Adjusted p-value') + theme_minimal()
ggExtra::ggMarginal(p, type = 'density', color='gray', fill='gray', size=10)## Warning: Removed 3871 rows containing missing values (geom_point).
rm(p)- There is a clear negative relation between lfc and mean expression, for both differentially expressed and not differentially expressed groups of genes
plot_data = data.frame('ID'=rownames(datExpr), 'meanExpr'=rowMeans(datExpr)) %>% left_join(DE_info, by='ID') %>%
mutate('statisticallySignificant'=padj<0.05 & !is.na(padj))
plot_data %>% ggplot(aes(meanExpr, abs(log2FoldChange), color=statisticallySignificant)) +
geom_point(alpha=0.1) + geom_smooth(method='lm') +
theme_minimal() + scale_y_sqrt() + theme(legend.position = 'bottom') +
xlab('Mean Expression') + ylab('abs(lfc)') + ggtitle('Log fold change by level of expression')
When filtering for differential expression, the points seem to separate ino two clouds depending on whether they are over or underexpressed
The top cloud corresponds to the over expressed genes and the bottom to the under expressed ones
datExpr_DE = datExpr[DE_info$significant,]
pca = datExpr_DE %>% prcomp
plot_data = cbind(data.frame('PC1'=pca$x[,1], 'PC2'=pca$x[,2]), DE_info[DE_info$significant==TRUE,])
pos_zero = -min(plot_data$log2FoldChange)/(max(plot_data$log2FoldChange)-min(plot_data$log2FoldChange))
p = plot_data %>% ggplot(aes(PC1, PC2, color=log2FoldChange)) + geom_point(alpha=0.5) +
scale_color_gradientn(colours=c('#F8766D','#faa49e','white','#00BFC4','#009499'),
values=c(0, pos_zero-0.1, pos_zero, pos_zero+0.1, 1)) +
theme_minimal() + ggtitle('
PCA of differentially expressed genes') + # This is on purpose, PDF doesn't save well without this white space (?)
xlab(paste0('PC1 (',round(100*summary(pca)$importance[2,1],1),'%)')) +
ylab(paste0('PC2 (',round(100*summary(pca)$importance[2,2],1),'%)')) +
theme(legend.position = 'bottom')
ggExtra::ggMarginal(p, type='density', color='gray', fill='gray', size=10)
rm(pos_zero, p)Separating the genes into these two groups: Salmon: under-expressed, aqua: over-expressed
plot_data = plot_data %>% mutate('Group'=ifelse(log2FoldChange>0,'overexpressed','underexpressed')) %>%
mutate('Group' = factor(Group, levels=c('underexpressed','overexpressed')))
plot_data %>% ggplot(aes(PC1, PC2, color=Group)) + geom_point(alpha=0.4) +
xlab(paste0('PC1 (',round(100*summary(pca)$importance[2,1],1),'%)')) +
ylab(paste0('PC2 (',round(100*summary(pca)$importance[2,2],1),'%)')) +
theme_minimal() + ggtitle('PCA')
rm(pca)Plotting the mean expression by group in Gandal’s dataset there seemed to exist underlying distributions, so we would use GMM to separate them, but everything seems very homogeneous here, so this doesn’t seem to be necessary. (If we do it anyway we can see that they still cluster by mean expression, which makes sense since it explains the majority of the variance of the genes)
- Under-expressed ASD genes tend to have a higher mean expression than over-expressed ones (I would have thought this would be the opposite way)
gg_colour_hue = function(n) {
hues = seq(15, 375, length = n + 1)
hcl(h = hues, l = 65, c = 100)[1:n]
}
tot_n_clusters = 4
plot_data = plot_data %>% mutate('MeanExpr'=rowMeans(datExpr_DE), 'SDExpr'=apply(datExpr_DE,1,sd))
GMM_G1 = plot_data %>% filter(Group=='overexpressed') %>% dplyr::select(MeanExpr) %>% GMM(2)
GMM_G2 = plot_data %>% filter(Group=='underexpressed') %>% dplyr::select(MeanExpr) %>% GMM(2)
memberships_G1 = data.frame('ID'=plot_data$ID[plot_data$Group=='overexpressed'],
'Membership'=GMM_G1$Log_likelihood %>%
apply(1, function(x) glue('over_', which.max(x))))
memberships_G2 = data.frame('ID'=plot_data$ID[plot_data$Group=='underexpressed'],
'Membership'=GMM_G2$Log_likelihood %>%
apply(1, function(x) glue('under_', which.max(x))))
plot_data = rbind(memberships_G1, memberships_G2) %>% left_join(plot_data, by='ID')## Warning: Column `ID` joining factor and character vector, coercing into
## character vectorp1 = plot_data %>% ggplot(aes(x=MeanExpr, color=Group, fill=Group)) + geom_density(alpha=0.4) +
theme_minimal() + theme(legend.position='bottom')
p2 = plot_data %>% ggplot(aes(x=MeanExpr)) +
stat_function(fun=dnorm, n=100, colour=gg_colour_hue(tot_n_clusters)[1],
args=list(mean=GMM_G1$centroids[1], sd=GMM_G1$covariance_matrices[1])) +
stat_function(fun=dnorm, n=100, colour=gg_colour_hue(tot_n_clusters)[2],
args=list(mean=GMM_G1$centroids[2], sd=GMM_G1$covariance_matrices[2])) +
stat_function(fun=dnorm, n=100, colour=gg_colour_hue(tot_n_clusters)[3],
args=list(mean=GMM_G2$centroids[1], sd=GMM_G2$covariance_matrices[1])) +
stat_function(fun=dnorm, n=100, colour=gg_colour_hue(tot_n_clusters)[4],
args=list(mean=GMM_G2$centroids[2], sd=GMM_G2$covariance_matrices[2])) +
theme_minimal()
p3 = plot_data %>% ggplot(aes(PC1, PC2, color=Membership)) + geom_point(alpha=0.4) + theme_minimal() +
theme(legend.position='bottom')
grid.arrange(p1, p2, p3, nrow=1)
rm(gg_colour_hue, GMM_G1, GMM_G2, memberships_G1, memberships_G2, p1, p2, p3, tot_n_clusters)For previous preprocessing pipelines, the pattern found above was also present in the standard deviation, but there doesn’t seem to be any distinguishable patterns now. This could be because the variance was almost homogenised with the vst normalisation algorithm.
plot_data %>% ggplot(aes(x=SDExpr, color=Group, fill=Group)) + geom_density(alpha=0.4) + theme_minimal()
rm(plot_data)Effects of modifying the log fold change threshold
fc_list = seq(1, 1.1, 0.005)
n_genes = nrow(datExpr)
# Calculate PCAs
datExpr_pca_samps = datExpr %>% data.frame %>% t %>% prcomp(scale.=TRUE)
datExpr_pca_genes = datExpr %>% data.frame %>% prcomp(scale.=TRUE)
# Initialice DF to save PCA outputs
pcas_samps = datExpr_pca_samps$x %>% data.frame %>% dplyr::select(PC1:PC2) %>%
mutate('ID'=colnames(datExpr), 'fc'=0, PC1=scale(PC1), PC2=scale(PC2))
pcas_genes = datExpr_pca_genes$x %>% data.frame %>% dplyr::select(PC1:PC2) %>%
mutate('ID'=rownames(datExpr), 'fc'=0, PC1=scale(PC1), PC2=scale(PC2))
pca_samps_old = pcas_samps
pca_genes_old = pcas_genes
for(fc in fc_list){
# Recalculate DE_info with the new threshold (p-values change) an filter DE genes
DE_genes = results(dds, lfcThreshold=log2(fc), altHypothesis='greaterAbs') %>% data.frame %>%
mutate('ID'=rownames(.)) %>% filter(padj<0.05)
datExpr_DE = datExpr %>% data.frame %>% filter(rownames(.) %in% DE_genes$ID)
n_genes = c(n_genes, nrow(DE_genes))
# Calculate PCAs
datExpr_pca_samps = datExpr_DE %>% t %>% prcomp(scale.=TRUE)
datExpr_pca_genes = datExpr_DE %>% prcomp(scale.=TRUE)
# Create new DF entries
pca_samps_new = datExpr_pca_samps$x %>% data.frame %>% dplyr::select(PC1:PC2) %>%
mutate('ID'=colnames(datExpr), 'fc'=fc, PC1=scale(PC1), PC2=scale(PC2))
pca_genes_new = datExpr_pca_genes$x %>% data.frame %>% dplyr::select(PC1:PC2) %>%
mutate('ID'=DE_genes$ID, 'fc'=fc, PC1=scale(PC1), PC2=scale(PC2))
# Change PC sign if necessary
if(cor(pca_samps_new$PC1, pca_samps_old$PC1)<0) pca_samps_new$PC1 = -pca_samps_new$PC1
if(cor(pca_samps_new$PC2, pca_samps_old$PC2)<0) pca_samps_new$PC2 = -pca_samps_new$PC2
if(cor(pca_genes_new[pca_genes_new$ID %in% pca_genes_old$ID,]$PC1,
pca_genes_old[pca_genes_old$ID %in% pca_genes_new$ID,]$PC1)<0){
pca_genes_new$PC1 = -pca_genes_new$PC1
}
if(cor(pca_genes_new[pca_genes_new$ID %in% pca_genes_old$ID,]$PC2,
pca_genes_old[pca_genes_old$ID %in% pca_genes_new$ID,]$PC2 )<0){
pca_genes_new$PC2 = -pca_genes_new$PC2
}
pca_samps_old = pca_samps_new
pca_genes_old = pca_genes_new
# Update DFs
pcas_samps = rbind(pcas_samps, pca_samps_new)
pcas_genes = rbind(pcas_genes, pca_genes_new)
}
# Add Diagnosis/SFARI score information
pcas_samps = pcas_samps %>% left_join(datMeta, by=c('ID')) %>%
dplyr::select(ID, PC1, PC2, fc, Diagnosis, brain_lobe)
# pcas_genes = pcas_genes %>% left_join(SFARI_genes, by='ID') %>%
# mutate('score'=as.factor(`gene-score`)) %>%
# dplyr::select(ID, PC1, PC2, lfc, score)
# Plot change of number of genes
ggplotly(data.frame('fc'=fc_list, 'n_genes'=n_genes[-1]) %>% ggplot(aes(x=fc, y=n_genes)) +
geom_point() + geom_line() + theme_minimal() + xlab('Fold Change') +
ggtitle('Number of remaining genes when modifying filtering threshold'))rm(fc_list, n_genes, fc, pca_samps_new, pca_genes_new, pca_samps_old, pca_genes_old,
datExpr_pca_samps, datExpr_pca_genes)Samples
Note: PC values get smaller as Log2 fold change increases, so on each iteration the values were scaled so it would be easier to compare between frames
Coloured by Diagnosis:
The lfc threshold doesn’t seem to make a big difference for differentiating genes by diagnosis
ggplotly(pcas_samps %>% ggplot(aes(PC1, PC2, color=Diagnosis)) + geom_point(aes(frame=fc, ids=ID)) +
theme_minimal() + ggtitle('Samples PCA plot modifying filtering threshold'))Coloured by brain region:
There doesn’t seem to be any recognisable pattern
ggplotly(pcas_samps %>% ggplot(aes(PC1, PC2, color=brain_lobe)) + geom_point(aes(frame=fc, ids=ID)) +
theme_minimal() + ggtitle('Samples PCA plot modifying filtering threshold'))Genes
ggplotly(pcas_genes %>% ggplot(aes(PC1, PC2)) + geom_point(aes(frame=fc, ids=ID, alpha=0.3)) +
theme_minimal() + ggtitle('Genes PCA plot modifying filtering threshold'))Session info
sessionInfo()## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/libopenblasp-r0.2.20.so
##
## locale:
## [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB.UTF-8 LC_COLLATE=en_GB.UTF-8
## [5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
## [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] parallel stats4 stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] DESeq2_1.24.0 SummarizedExperiment_1.14.1
## [3] DelayedArray_0.10.0 BiocParallel_1.18.1
## [5] matrixStats_0.54.0 Biobase_2.44.0
## [7] GenomicRanges_1.36.0 GenomeInfoDb_1.20.0
## [9] IRanges_2.18.2 S4Vectors_0.22.0
## [11] BiocGenerics_0.30.0 ClusterR_1.2.1
## [13] gtools_3.8.1 Rtsne_0.15
## [15] GGally_1.4.0 gridExtra_2.3
## [17] viridis_0.5.1 viridisLite_0.3.0
## [19] RColorBrewer_1.1-2 plotlyutils_0.0.0.9000
## [21] plotly_4.9.0 glue_1.3.1
## [23] reshape2_1.4.3 forcats_0.4.0
## [25] stringr_1.4.0 dplyr_0.8.2
## [27] purrr_0.3.3 readr_1.3.1
## [29] tidyr_0.8.3 tibble_2.1.3
## [31] ggplot2_3.2.0 tidyverse_1.2.1
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 htmlTable_1.13.1 XVector_0.24.0
## [4] base64enc_0.1-3 rstudioapi_0.10 bit64_0.9-7
## [7] AnnotationDbi_1.46.1 lubridate_1.7.4 xml2_1.2.2
## [10] splines_3.6.1 geneplotter_1.62.0 knitr_1.23
## [13] zeallot_0.1.0 Formula_1.2-3 jsonlite_1.6
## [16] broom_0.5.2 annotate_1.62.0 cluster_2.1.0
## [19] shiny_1.3.2 compiler_3.6.1 httr_1.4.0
## [22] backports_1.1.4 assertthat_0.2.1 Matrix_1.2-18
## [25] lazyeval_0.2.2 cli_1.1.0 later_0.8.0
## [28] acepack_1.4.1 htmltools_0.3.6 tools_3.6.1
## [31] gmp_0.5-13.5 gtable_0.3.0 GenomeInfoDbData_1.2.1
## [34] Rcpp_1.0.1 cellranger_1.1.0 vctrs_0.2.0
## [37] nlme_3.1-142 crosstalk_1.0.0 xfun_0.8
## [40] rvest_0.3.4 miniUI_0.1.1.1 mime_0.7
## [43] XML_3.98-1.20 zlibbioc_1.30.0 scales_1.0.0
## [46] promises_1.0.1 hms_0.5.1 yaml_2.2.0
## [49] memoise_1.1.0 rpart_4.1-15 ggExtra_0.9
## [52] reshape_0.8.8 latticeExtra_0.6-28 stringi_1.4.3
## [55] RSQLite_2.1.2 genefilter_1.66.0 checkmate_1.9.4
## [58] rlang_0.4.2 pkgconfig_2.0.2 bitops_1.0-6
## [61] evaluate_0.14 lattice_0.20-38 labeling_0.3
## [64] htmlwidgets_1.3 bit_1.1-14 tidyselect_0.2.5
## [67] plyr_1.8.4 magrittr_1.5 R6_2.4.0
## [70] generics_0.0.2 Hmisc_4.2-0 DBI_1.0.0
## [73] pillar_1.4.2 haven_2.1.1 foreign_0.8-72
## [76] withr_2.1.2 survival_3.1-7 RCurl_1.95-4.12
## [79] nnet_7.3-12 modelr_0.1.5 crayon_1.3.4
## [82] rmarkdown_1.13 locfit_1.5-9.1 grid_3.6.1
## [85] readxl_1.3.1 data.table_1.12.2 blob_1.2.0
## [88] digest_0.6.19 xtable_1.8-4 httpuv_1.5.1
## [91] munsell_0.5.0